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#1 2012-10-15 15:58:02

Agnishom
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Integer Factorisation

Prove the following:
If:


where p are prime numbers
Then:


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Who are you to judge everything?' -Alokananda

#2 2012-10-15 20:54:41

scientia
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Re: Integer Factorisation

Agnishom wrote:

Prove the following:
If:


where p are distinct prime numbers
Then:


Let
denote the number of positive factors of
.

It's obvious that if
and
have no factor in common other than 1, then
.

Also the factors of
are
and so
.

Combining the two observations above gives the required solution.

#3 2012-10-15 21:29:19

bob bundy
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Re: Integer Factorisation

hi scientia

Nice proof!  smile

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

#4 2012-10-15 22:05:15

Agnishom
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Re: Integer Factorisation

Thanks @scientia


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Who are you to judge everything?' -Alokananda

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